More on the Minimum Size of Graphs with Given Rainbow Index

More on the Minimum Size of Graphs with Given Rainbow Index

The concept of k-rainbow index rxk(G) of a connected graph G, introduced by Chartrand et al., is a natural generalization of the rainbow connection number of a graph. Liu introduced a parameter t(n, k, ℓ) to investigate the problems of the minimum size of a connected graph with given order and k-rai...

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Bibliographic Details
Main Author: Zhao Yan
Format: Article
Language:English
Published: Sciendo 2020-02-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
steiner distance
rainbow s-tree
k-rainbow index
05c05
05c15
05c75
Online Access:https://doi.org/10.7151/dmgt.2131
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spelling doaj-842ea84b6bfe46dd91d5dbdcc4f38a082021-09-05T17:20:24ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922020-02-0140122724110.7151/dmgt.2131dmgt.2131More on the Minimum Size of Graphs with Given Rainbow IndexZhao Yan0Department of Mathematics, Taizhou University, Taizhou225300, P.R. ChinaThe concept of k-rainbow index rxk(G) of a connected graph G, introduced by Chartrand et al., is a natural generalization of the rainbow connection number of a graph. Liu introduced a parameter t(n, k, ℓ) to investigate the problems of the minimum size of a connected graph with given order and k-rainbow index at most ℓ and obtained some exact values and upper bounds for t(n, k, ℓ). In this paper, we obtain some exact values of t(n, k, ℓ) for large ℓ and better upper bounds of t(n, k, ℓ) for small ℓ and k = 3.https://doi.org/10.7151/dmgt.2131steiner distancerainbow s-treek-rainbow index05c0505c1505c75
collection DOAJ
language English
format Article
sources DOAJ
author Zhao Yan
spellingShingle Zhao Yan
More on the Minimum Size of Graphs with Given Rainbow Index
Discussiones Mathematicae Graph Theory
steiner distance
rainbow s-tree
k-rainbow index
05c05
05c15
05c75
author_facet Zhao Yan
author_sort Zhao Yan
title More on the Minimum Size of Graphs with Given Rainbow Index
title_short More on the Minimum Size of Graphs with Given Rainbow Index
title_full More on the Minimum Size of Graphs with Given Rainbow Index
title_fullStr More on the Minimum Size of Graphs with Given Rainbow Index
title_full_unstemmed More on the Minimum Size of Graphs with Given Rainbow Index
title_sort more on the minimum size of graphs with given rainbow index
publisher Sciendo
series Discussiones Mathematicae Graph Theory
issn 2083-5892
publishDate 2020-02-01
description The concept of k-rainbow index rxk(G) of a connected graph G, introduced by Chartrand et al., is a natural generalization of the rainbow connection number of a graph. Liu introduced a parameter t(n, k, ℓ) to investigate the problems of the minimum size of a connected graph with given order and k-rainbow index at most ℓ and obtained some exact values and upper bounds for t(n, k, ℓ). In this paper, we obtain some exact values of t(n, k, ℓ) for large ℓ and better upper bounds of t(n, k, ℓ) for small ℓ and k = 3.
topic steiner distance
rainbow s-tree
k-rainbow index
05c05
05c15
05c75
url https://doi.org/10.7151/dmgt.2131
work_keys_str_mv AT zhaoyan moreontheminimumsizeofgraphswithgivenrainbowindex
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